# Q.5.    A person needs a lens of power –5.5 dioptres for correcting his distant vision. For correcting his near vision he needs a lens of power +1.5 dioptre. What is the focal length of the lens required for correcting (i) distant vision, and (ii) near vision?

D Divya Prakash Singh

For the distant vision:

The power of the lens, given $P = -5.5\ D$

$Power(in\ D) = \frac{1}{f(m)}$

Hence the focal length will be:

$f= \frac{100}{-5.5} = -18.2\ cm$

Therefore, the focal length of the lens required for correcting distant vision will be:$-18.2\ cm$ (Here, the negative sign of focal length tells us that it is a concave lens).

For near vision:

The power of the lens, given $P = +1.5\ D$

$Power(in\ D) = \frac{1}{f(m)}$

Hence the focal length will be:

$f= \frac{100}{+1.5} = 66.66\ cm$

Therefore, the focal length of the lens required for correcting near vision will be:$+66.7\ cm$ (Here, the positive sign of focal length tells us that it is a convex lens).

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